Being invisible ad libitum has long captivated the popular imagination, particularly in terms of safeguarding modern high-end instruments from potential threats. Decades ago, the advent of metamaterials and transformation optics sparked considerable interest in invisibility cloaks, which have been mainly demonstrated in ground and waveguide modalities. However, an omnidirectional flying cloak has not been achieved, primarily due to the challenges associated with dynamic synthesis of metasurface dispersion. We demonstrate an autonomous aeroamphibious invisibility cloak that incorporates a suite of perception, decision, and execution modules, capable of maintaining invisibility amidst kaleidoscopic backgrounds and neutralizing external stimuli. The physical breakthrough lies in the spatiotemporal modulation imparted on tunable metasurfaces to sculpt the scattering field in both space and frequency domains. To intelligently control the spatiotemporal metasurfaces, we introduce a stochastic-evolution learning that automatically aligns with the optimal solution through maximum probabilistic inference. In a fully self-driving experiment, we implement this concept on an unmanned drone and showcase adaptive invisibility in three canonical landscapes—sea, land, and air—with a similarity rate of up to 95%. Our work extends the family of invisibility cloaks to flying modality and inspires other research on material discoveries and homeostatic meta-devices.